Can a Self-Exciting Jump Structure Better Capture the Jump Behavior of Cryptocurrencies? A Comparative Analysis with the S&P 500

Abstract

This paper introduces a stochastic volatility model with an independent self-exciting jump structure model (SE-SVIJ) to capture the jump dynamics of cryptocurrency daily returns. The empirical results show that the SE-SVIJ model can provide a less volatile and less persistent volatility process. We find clear evidence of self-exciting jump clustering in the cryptocurrency market. The SE-SVIJ model identifies more jumps than the stochastic volatility model with independent jumps (SVIJ). We also conduct a comparison between the cryptocurrency and S&P 500 markets in terms of jump behavior: S&P 500 returns have more frequent negative jumps and larger negative jumps on average. In comparison, the cryptocurrency markets suffer from positive jumps continuously, and also suffer from an interaction effect between positive and negative jumps during the high-volatility regime. We also demonstrate the effectiveness of the SE-SVIJ model in modeling cryptocurrency return and volatility, as reflected by volatility comparisons and tail fitting.

Keywords: Cryptocurrency, Stochastic volatility, Self-exciting jumps, Bayesian estimation, S&P 500